Geometric Methods in Inverse Problems and PDE Control

  • Christopher B. Croke
  • Michael S. Vogelius
  • Gunther Uhlmann
  • Irena Lasiecka

Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 137)

Table of contents

  1. Front Matter
    Pages i-x
  2. James G. Berryman, Liliana Borcea, George C. Papanicolaou, Chrysoula Tsogka
    Pages 15-24
  3. Kurt Bryan, Michael S. Vogelius
    Pages 25-46
  4. Christopher B. Croke
    Pages 47-72
  5. Michael Taylor
    Pages 257-262
  6. Gunther Uhlmann
    Pages 263-287
  7. Back Matter
    Pages 323-329

About these proceedings

Introduction

This volume contains a slected number of articles based on lectures delivered at the IMA 2001 Summer Program on Geometric Methods in Inverse Problems and PDE Control. This program was focused on a set of common tools that are used in the study of inverse coefficient problems and control problems for partial differential equations, and in particular on their strong relation to fundamental problems of differential geometry. Examples of such tools are Dirichlet-to-Neumann data boundary maps, unique continuation results, Carleman estimates, microlocal analysis and the so-called boundary control method. Examples of intimately connected fundamental problems in differential geometry are the boundary rigidity problem and the isospectral problem. The present volume provides a broad survey of recent progress concerning inverse and control problems for PDEs and related differential geometric problems. It is hoped that it will also serve as an excellent ``point of departure" for researchers who will want to pursue studies at the intersection of these mathematically exciting, and practically important subjects.

Keywords

PDE control Riemannian geometry differential geometry inverse problems manifold partial differential equation

Editors and affiliations

  • Christopher B. Croke
    • 1
  • Michael S. Vogelius
    • 2
  • Gunther Uhlmann
    • 3
  • Irena Lasiecka
    • 4
  1. 1.Department of MathematicsUniversity of PennsylvaniaPhiladelphiaUSA
  2. 2.Department of MathematicsRutgers UniversityNew BrunswickUSA
  3. 3.Department of MathematicsUniversity of WashingtonSeattleUSA
  4. 4.Department of MathematicsUniversity of VirginiaCharlottesvilleUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4684-9375-7
  • Copyright Information Springer-Verlag New York 2004
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4419-2341-7
  • Online ISBN 978-1-4684-9375-7
  • Series Print ISSN 0940-6573
  • About this book
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